Geometry and Topology Seminar: October 4, 2024
Speaker: Sofia Martinez Alberga (Purdue University)
Title: Modeling Equivariant Simplicial Sets with Simplicial Coalgebras
Abstract: Given a commutative ring R, a $\pi_1$-R-equivalence is a continuous map of spaces inducing an isomorphism on fundamental groups and an R-homology equivalence between universal covers. When R is an algebraically closed field, Raptis and Rivera described a full and faithful model for the homotopy theory of spaces up to $\pi_1$-R-equivalence. They did
this by means of simplicial coalgebras considered up to a notion of weak equivalence created by a localized version of the cobar functor. In this article, we prove a G-equivariant analog of this statement using generalizations of a celebrated theorem of Elmendorf. We also prove a more general result about modeling $G$-simplicial sets considered under a linearized version of quasi-categorical equivalence in terms of simplicial coalgebras.
Contact: Hannah Housden